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The deviation of the density of the minor block from its value in the uniform, disordered state is an oscillatory function and includes both excess and depletion in equal amount; the use of the absolute value in the definition of the material excess counts both contributions. Thus, 2π instead of 4π is used to correct for this double counting. However, this is purely a matter of convention; a material excess with the factor of 4π would have been an equally valid definition of the order parameter.
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This statement implicitly assumes that the pathway for the formation and dissociation of a micelle is properly described by the "reaction coordinate" of Figure 1. We believe this assumption to be physically reasonable; however, its rigorous justification would require analyzing the actual kinetics of the formation and dissociation of a micelle, which is beyond the scope of this work.
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m). We thank Prof. David Morse for a helpful discussion on this point.
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